1. Multiple choice questions: (There are 6 questions in this big question, 4 points for each question, out of 24 points).
1. Among the following equations, the simplest quadratic root is (? )
(1)? ; ? (B)？ ; (3)? ; ? (D)3( 1)。
2. The following unary quadratic equation about X with real roots is (? )
(1); (b) and: (c)? ; (4).
3. If the parabola moves downward by 1 unit, the expression of the new parabola is (? )
(1); (b) and: (c) and: (4).
4.data? 0, 1, 1,3,3,4? The median and average of is (? )
(1)? 2 and 2.4; (B)2 and 2? ; (C) 1 and 2; ? Articles 3 and 2.
5. As shown in figure 1, it is known that in △ABC, points D, E and F are points on the sides of AB, AC and BC respectively.
DE∨BC, EF∨AB, and AD: DB? =? 3: 5, then cf: CB is equal to ()
(1)? 5∶8? ; ? (B)3∶8； (3)? 3∶5? ; (D)2∶5。
6. In trapezoidal ABCD, AD∑BC, diagonal AC and BD intersect at point O, under the following conditions,
Can we judge that the trapezoid ABCD is an isosceles trapezoid? )
∠BDC？ =∠BCD； (B)∠ABC？ =∠DAB； (c) Asian Development Bank? =∠DAC； ∠AOB？ =∠BOC。
Two. Fill in the blanks: (This topic is entitled *** 12, with 4 points for each question, out of 48 points)
7. Factorization: =? _____________.？ 8. Unequal groups? The solution set of is _ _ _ _ _ _.
9. Calculation: =? ___________.？ 10. Calculation: 2? (─)? +? 3=? ___________.
1 1. Known functions? And then what? __________.
12. Write the seven letters in the English word theorem on seven identical cards, put them down on the table casually, and choose any one, then the probability of getting the letter E is _ _ _ _ _ _ _ _.
13. The enrollment numbers of four interest groups A, B, C and D in a school are shown in Figure 2, so the sum of enrollment numbers of groups A and C accounts for _ _ _ _ _ _.
[Source: Xueke. com z x x k]
14. In ⊙, it is known that the radius length is 3 and the chord length is 4, so the distance from the center of the circle is _ _ _ _ _ _ _ _.
15. As shown in Figure 3, in △ and △, points B, F, C and E are on the same straight line, BF? =? CE, AC∨DF, please add a condition to make △△, and the added condition can be _ _ _ _ _ _ _ _. Just write one, without auxiliary lines.
16. Miss Li drives from place A to place B, which is 240 kilometers away. What if there is still oil in the mailbox? (liters) and mileage? (km) is a linear function, and the image is shown in Figure 4, so the remaining oil in the mailbox is _ _ _ _ _ _ _ liter when it reaches the second place.
17. When an internal angle α in a triangle is twice that of another internal angle β, we call this triangle a "characteristic triangle", where α is called a "characteristic angle". If the "characteristic angle" of a "characteristic triangle" is 100, then the degree of the minimum internal angle of this "characteristic triangle" is _ _ _ _ _
18. As shown in Figure 5, in △,,? Tan? c？ =? 2(3), if δ
After folding along the straight line L, the point falls at the midpoint of the edge, and the straight line L intersects the edge at the point.
Then the length is _ _ _ _ _ _ _.
Third, answer: (This big question is ***7 questions, out of 78 points)
(This big problem ***7, 19~22, 10, 23 and 24, 12, 25, 14, out of 48).
19. Calculation: 20. Solve the equation:? .
2 1. Known plane rectangular coordinate system (as shown in Figure 6), straight line? famous book
Passing through the first, second and third quadrants and intersecting with the Y axis, the point (2, t) is on this straight line.
The area delta of the connection is equal to 1.
( 1);
(2) If the inverse proportional function (is constant,)
Like this point, find the analytical expression of this inverse proportional function.
22. As shown in Figure 7- 1, the "two-section railing" at the exit of the underground garage, the point is the fulcrum of the railing rotation and the point is the connection point of the two sections of railing. When the vehicle passes, the position where the railing rises is shown in Figure 7-2, and its schematic diagram is shown in Figure 7-3, in which ⊥,
∨,, meters, find the height of rail EF section from the ground when the vehicle passes (that is, the distance from any point on the straight line EF to the straight line BC).
(The result is accurate to 0. 1m, ignoring the railing width. Reference data: sin? 37 ? ≈? 0.60，cos？ 37 ? ≈? 0.80, Tan? 37 ? ≈? 0.75.)
23. As shown in Figure 8, at △,,? That is the midpoint of the edge and intersects it.
The intersecting extension lines are at points.
(1) Verification:;
(2) Connect and cross vertical lines composed of points.
Extend the line to point, verify:.
24. As shown in Figure 9, in the plane rectangular coordinate system, a parabola with vertex passes through the point and the point on the positive semi-axis of the shaft, =? 2,.
(1) Find the expression of this parabola;
(2) Add and find the size;
(3) If the point is on the axis and △ is similar to △, find the coordinates of the point.
25. In a rectangle, a point is a moving point on the edge, and the vertical line of a line segment is connected with the point.
The vertical foot is a point and connected (as shown in figure 10).
(1), and write the range of values;
(2) The required value when ⊙P with the radius of length and ⊙Q with the radius of length are circumscribed;
(3) The point is on the edge, and the vertical line passing through the point is the value of if, if.